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The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results.

A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces